{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WCBC5GDV3BRYRBM2JKTC6JCUTN","short_pith_number":"pith:WCBC5GDV","schema_version":"1.0","canonical_sha256":"b0822e9875d86388859a4aa62f24549b45962a4e83a663c4bef17b559bf96f99","source":{"kind":"arxiv","id":"1803.09538","version":1},"attestation_state":"computed","paper":{"title":"Determining a fractional Helmholtz system with unknown source and medium parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Xinlin Cao","submitted_at":"2018-03-26T12:13:59Z","abstract_excerpt":"We are concerned with an inverse problem associated with the fractional Helmholtz system that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that both the medium parameter and the internal source of the wave equation are unknown. Moreover, we consider a general class of source functions which can be frequency-dependent. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp cont"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.09538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-26T12:13:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d33438b4d5af8162ac21c6e0e36a408ddaee98a8cf3dd46521e27766e42ec999","abstract_canon_sha256":"b8ebe2d74369c0b2a35b431b49a88df8f13b57cd83e483ce4233d9206e31d9a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:11.200600Z","signature_b64":"INgfAmpR6Yj3nwJwzdmxpmkwGxu4TJ8mbTV0bYwILkP7zLeVAsvxR8QDBjvh52/0BLoBrkfWIlyfBPbZsDZgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0822e9875d86388859a4aa62f24549b45962a4e83a663c4bef17b559bf96f99","last_reissued_at":"2026-05-18T00:20:11.199868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:11.199868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determining a fractional Helmholtz system with unknown source and medium parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Xinlin Cao","submitted_at":"2018-03-26T12:13:59Z","abstract_excerpt":"We are concerned with an inverse problem associated with the fractional Helmholtz system that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that both the medium parameter and the internal source of the wave equation are unknown. Moreover, we consider a general class of source functions which can be frequency-dependent. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09538","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.09538","created_at":"2026-05-18T00:20:11.199970+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09538v1","created_at":"2026-05-18T00:20:11.199970+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09538","created_at":"2026-05-18T00:20:11.199970+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCBC5GDV3BRY","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCBC5GDV3BRYRBM2","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCBC5GDV","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN","json":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN.json","graph_json":"https://pith.science/api/pith-number/WCBC5GDV3BRYRBM2JKTC6JCUTN/graph.json","events_json":"https://pith.science/api/pith-number/WCBC5GDV3BRYRBM2JKTC6JCUTN/events.json","paper":"https://pith.science/paper/WCBC5GDV"},"agent_actions":{"view_html":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN","download_json":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN.json","view_paper":"https://pith.science/paper/WCBC5GDV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09538&json=true","fetch_graph":"https://pith.science/api/pith-number/WCBC5GDV3BRYRBM2JKTC6JCUTN/graph.json","fetch_events":"https://pith.science/api/pith-number/WCBC5GDV3BRYRBM2JKTC6JCUTN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN/action/storage_attestation","attest_author":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN/action/author_attestation","sign_citation":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN/action/citation_signature","submit_replication":"https://pith.science/pith/WCBC5GDV3BRYRBM2JKTC6JCUTN/action/replication_record"}},"created_at":"2026-05-18T00:20:11.199970+00:00","updated_at":"2026-05-18T00:20:11.199970+00:00"}